Year: 2012
Numerical Mathematics: Theory, Methods and Applications, Vol. 5 (2012), Iss. 4 : pp. 592–601
Abstract
We present a simple yet effective and applicable scheme, based on quadrature, for constructing optimal iterative methods. According to the, still unproved, Kung-Traub conjecture an optimal iterative method based on $n+1$ evaluations could achieve a maximum convergence order of $2^n$. Through quadrature, we develop optimal iterative methods of orders four and eight. The scheme can further be applied to develop iterative methods of even higher orders. Computational results demonstrate that the developed methods are efficient as compared with many well known methods.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2012.m1114
Numerical Mathematics: Theory, Methods and Applications, Vol. 5 (2012), Iss. 4 : pp. 592–601
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Iterative methods fourth order eighth order quadrature Newton convergence nonlinear optimal.
-
Second Derivative Free Eighteenth Order Convergent Method for Solving Non-Linear Equations
Kumar Vatti, V.B. | Sri, Ramadevi | Mylapalli, M.S.KumarOriental journal of computer science and technology, Vol. 10 (2017), Iss. 04 P.829
https://doi.org/10.13005/ojcst/10.04.19 [Citations: 0] -
Eighteenth Order Convergent Method for Solving Non-Linear Equations
Vatti, V.B | Sri, Ramadevi | Mylapalli, M.SOriental journal of computer science and technology, Vol. 10 (2017), Iss. 1 P.144
https://doi.org/10.13005/ojcst/10.01.19 [Citations: 1] -
Harmony Search and Nature Inspired Optimization Algorithms
Second Derivative-Free Two-Step Extrapolated Newton’s Method
Kumar Vatti, V. B. | Sri, Ramadevi | Kumar Mylapalli, M. S.2019
https://doi.org/10.1007/978-981-13-0761-4_101 [Citations: 0]